stalkClosedPointTo_comp — Mathlib

English

The closed-point stalk map is compatible with composition: stalkClosedPointTo(f ≫ g) = g.stalkMap ≫ stalkClosedPointTo f.

Русский

Сопоставление стоячей точки замкнутой точки совместимо с композициями: stalkClosedPointTo(f ≫ g) = g.stalkMap ≫ stalkClosedPointTo f.

LaTeX

$$$\\operatorname{stalkClosedPointTo}(f \\circ g) = g\\,\\mathrm{stalkMap} \\;\\circ \\operatorname{stalkClosedPointTo} f$$$

Lean4

theorem stalkClosedPointTo_comp (g : X ⟶ Y) : stalkClosedPointTo (f ≫ g) = g.stalkMap _ ≫ stalkClosedPointTo f :=
  by
  rw [stalkClosedPointTo, Scheme.stalkMap_comp]
  exact Category.assoc _ _ _

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